Four FORTRAN Programs for Numerically Solving Helholtz's Equation in an Arbitrary Bounded Planar Region

摘要

In recent years special techniques known as the capacitance matrix methods (CMM) have been developed for the numerical solution of Helmholtz's equation in a general bounded planar region - delta u + cu = f in omega , where c is a real constant, with either Dirichlet or Neumann conditions on the boundary. These methods make use of fast solvers in regions that allow for the separation of variables. There are two major variants of such methods: one in which the capacitance matrix is actually generated and LU-factored, and the other in which the capacitance matrix is used implicitly to compute a matrix-vector product in an iterative process. Explicit CMM are designed for repetitive use, i.e., with different functions f (while the constant c, the geometry of the problem and the mesh are unchanged). An important advantage of a CMM program is that it can be speeded up whenever a new and faster separable solver is available, by replacing a proper subroutine. A collection of four FORTRAN programs is presented: HLMHLZ is an implicit solver, recommemded for use when only one problem is to be solved or the amount of available core storage is limited; HELMIT is an explicit solver for general use when the same problem is to be solved with different functions f; HELSIX is a high-order explicit Poisson solver (with Dirichlet conditions only); HELSYM is an explicit solver for use in solving eigenvalue problems (with zero Dirichlet conditions only. These programs are limited to two-dimensional regions. 1 figure, 5 tables. (ERA citation 03:042089)